Limit Probabilities for Critical Age Dependent Branching Processes with Immigration.

摘要

Let Z sub O(t), N sub O (t) denote, respectively, the number of cells alive at t and the total progeny born by t in a process with a random number of new cells introduced at renewal epochs, each new cell initiating a critical age-dependent branching process. As t approaches infinity, the forms of P(Z sub O (t) = k) and P(N sub O (t) = k) are obtained for k = 1,2,... and k = 0,1,2,..., respectively. A multi-dimensional version and extension are indicated.